Question

Round tube made from A-36 steel OD & Wall thickness are provided in the question Use the following values: OD = 32 mm, wall thickness = 3 mm, L = 575 mm, P = 750 N. Determine the following. Give magnitudes only and do NOT include negative signs Notice the required units and provide at least 3 significant figures. Assume no yielding occurs. Maximum normal stress = Number MPa Maximum deflection (assume no yielding) = Number mm Is the "No Yield" assumption correct? Number (Type number 1 for yes and number 0 for no)

Answer 1

Title - Strength of Materials

Solution: Giren: Material: A-36 steel Young's modulus, E= 200 G fa for A-36 steel from standard data book. Outer Diameter = OD = 32 mm t, Thickness - 3 mm Length , L = 575 mm Load , P=750N To find: a) maximum b) Manimum Normal Stress in mpa Deflection in mm c) Is 'No Yielding' assumption correct ? Steps : a) Inner Diameter, ID = OD-2t ID = 32 - 2 (3) ID = 26 mm

Giren Beami P = 750N Ha . Va By static Equilibrium Conditions, EFx=0 Ha=ON { Fy =o . Va – 750 + Vb=0 :: Va + Vb = 750 EMARO .: 750 X (575) + Vb X 575 = 0 - V6 = 375 N Va = 375 N

can be calculated using Flexural Normal stress Formula, м - с I y Here, M = Maximum Bending moment .: M = 375 X 1575 M = 107812.5 N-mm about Neutral Anis I = moment of Inertia .: I = I LOD" -ID"] II [ 324- 264] I - 29040.09 mm4 here, y = distance of extreme end fibre of beam from neutra anis yo - 32 16 mm

... By flexural formula, o= Moy I 0 = 107812.5 X 16 29040.09 1:0= 59.400 MPa T ... (Answer of a)) To find Maximum Deflection in mm: By formula : For one end and other end support. having pinjoint having Roller Man. Deflection , s = max PL² 48.E. I .: Smau = 750 x (575)3 48 x 200x10°X 29040.09 .: Smax = 0.511 mm . (Answer of b))

c) The no yield assumption is not correct because for no yielding, the value of deflection must have to be zero. But here we see that there is a positive value of deflection, this indicates that there is a change in dimension , ie. presence of strain and ress is induced without yielding , thus bending stress is induced. Without thus no induction of there would be no strain and stress would have taken place.

Conclusion - Strength of Materials is the subject that deals with stresses in beam, deflections and the mechanical properties that vary due to loading and other system of forces. Yielding is the phenomenon where structure changes its dimensions but within the elastic limits so that it can get back to its original dimensions after the removal of loading on it. On crossing yield point, the material enters plastic region from where it starts to deform permanently.

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